After making the table using the given ratios we can conclude that Miguel will save $90 if he earns $120.00.
What do we mean by ratios?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For example, you might write the ratio as 1: 3 (there are 3 girls for every guy), which would suggest that there are 1 in 4 boys and 3 in 4 girls.
By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B).
So, the solution in the form of a table would be:
Money Earned Money saved Ratio
10 7.5 3/4
50 37.5 3/4
120 ? 3/4
150 112.5 3/4
? /120 = 3/4 => ? = 90
Miguel will save $90 if he earns $120.00.
Therefore, after making the table using the given ratios we can conclude that Miguel will save $90 if he earns $120.00.
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Correct question:
Miguel created the ratio table below to show how he uses the money he earns at work. Miguel’s Money Money Earned Money Saved $10.00 $7.50 $50.00 $37.50 $120.00? $150.00 $112.50 How much money will he save if he earns $120.00? $30.00 $45.00 $90.00 $75.00
Suppose that f(4)=2, g(4)=5, f'(4)=6, g'(4)=-3, f'(5)=8, and g'(2)=10.
Find h'(4) where
(a) h(x)=f(x)g(x)
(b) h(x)= g(x)/f(x)+g(x)
(c) h(x)=f(g(x))
please help
(a) Using the product rule for h(x) = f(x)g(x), h'(4) = 24
(b) Using the quotient rule, for h(x) = g(x) / (f(x) + g(x)), h'(4) = -33/49.
(c) Using chain rule for h(x) = f(g(x)), h'(4) = 80.
What is the solution of the functions?
We can use the product rule, quotient rule, and chain rule to find the derivatives of the functions h(x).
(a) h(x) = f(x)g(x)
Using the product rule, we have:
h'(x) = f'(x)g(x) + f(x)g'(x)
At x = 4, we have:
h'(4) = f'(4)g(4) + f(4)g'(4) = 6(5) + 2(-3) = 24
Therefore, h'(4) = 24.
(b) h(x) = g(x) / (f(x) + g(x))
Using the quotient rule, we have:
h'(x) = [g'(x)(f(x) + g(x)) - g(x)f'(x)] / (f(x) + g(x))^2
At x = 4, we have:
h'(4) = [g'(4)(f(4) + g(4)) - g(4)f'(4)] / (f(4) + g(4))^2
= [(-3)(2 + 5) - 5(6)] / (2 + 5)^2
= -33 / 49
Therefore, h'(4) = -33/49.
(c) h(x) = f(g(x))
Using the chain rule, we have:
h'(x) = f'(g(x))g'(x)
At x = 4, we have:
h'(4) = f'(g(4))g'(4)
= f'(5)(10)
= 8(10)
= 80
Therefore, h'(4) = 80.
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Circular sector with a radius of 12 inches and a central angle of 120 degrees
Answer:
hope this helps
Step-by-step explanation:
The circle below is centred at O.
a) Work out the size of angle X.
b) Which of the circle theorems below allows you to calculate this angle?
Answer:
61∘
Step-by-step explanation:
Isosceles triangle property:
The triangle in the circle is an isosceles triangle, so that means the lateral sides of the triangle are equal, and so are the angles;
x = 90∘ - 29∘ = 61∘ (90∘, because the tangent and the radius form a right angle (that the b) part, I think))
Replace each * with a digit that makes the solution of the equation a whole number. Find all possibilities.
5x – 124=10*
Answer:* = 50
Step-by-step explanation:
x = 75.2 5x -124 =500
10 times 50 =500
Please answer fast!!
Answer:
Look at the green dot
Step-by-step explanation:
The ratio of monthly income to the monthly saving of a family is 9:2. If the
saving is Rs 4,320, find the income and expenditure of the family.
Step-by-step explanation:
Let's assume that the monthly income of the family is x.
From the problem statement, we know that the ratio of monthly income to the monthly saving is 9:2.
Therefore, we can write:
x/4320 = 9/2
To solve for x, we can cross-multiply:
2x = 9*4320
2x = 38,880
x = 19,440
So, the monthly income of the family is Rs 19,440.
To find the monthly expenditure, we can subtract the monthly savings from the monthly income:
Monthly expenditure = Monthly income - Monthly saving
Monthly expenditure = 19,440 - 4,320
Monthly expenditure = 15,120
Therefore, the monthly expenditure of the family is Rs 15,120
Roman opened a savings account and started out the account with $45. He adds $18 each month. He currently has $207 in his account. How many months has he been saving?
Answer:
9
Step-by-step explanation: each month adding 18 starting at 45 and currently at 207 means he gained 162 and divided by 18,9 months.
Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.50 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $74.10. How much does an average movie ticket cost in each of these countries?
The average movie ticket cost in Switzerland and Japan each of these countries is 46.97.
Let's assume that the average cost of a movie ticket in Japan is x, and the average cost of a movie ticket in Switzerland is y.
According to the problem statement, we can write two equations based on the given information:
3x + 2y = 78.5 ...(1)
2x + 3y = 74.1 ...(2)
We can solve these equations simultaneously to find the values of x and y. Here's how:
Multiply equation (1) by 2 and equation (2) by 3, then subtract equation (1) from equation (2):
(2x + 3y) - 2(3x + 2y) = 74.1 - 2(78.5)
Simplifying this equation, we get:
-y = -109.3
Therefore, y = 109.3.
Now substitute y = 109.3 into either equation (1) or (2) and solve for x:
3x + 2(109.3) = 78.5
Simplifying this equation, we get:
3x = -140.9
Therefore, x = -46.97.
However, we cannot have negative ticket prices.
Therefore, the average cost of a movie ticket is 46.97.
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Type the correct answer in each box.
Compete the statement about these similar cylinders.
Figure 1
D.
9 in
E 4.5 in
5 in
Figure 2
P.
R
The circumference of the base of figure 2 is
(Hint: The circumference of a circle = 2rr and the area of a circle = n², where r is the radius.)
and the area of a
It inches, and the area of the base of figure 2 is
[]
π square inches.
Therefore, the completed statement is: The circumference of the base of Figure 2 is 9π inches, and the area of the base of Figure 2 is 20.25π square inches.
What is area?Area is a measure of the size of a two-dimensional surface or region, typically expressed in square units. It is the amount of space inside a closed shape, such as a square, rectangle, triangle, circle, or any other shape with a well-defined boundary. The concept of area is used in many areas of mathematics, science, and engineering, such as geometry, calculus, physics, and architecture. For example, engineers need to calculate the area of materials, such as the cross-sectional area of a pipe or the surface area of a building, in order to design structures that are strong, efficient, and safe.
Here,
The missing information in the statement can be found by using the given dimensions of the cylinders.
Figure 1 has a height of 9 inches and a radius of 4.5 inches.
Figure 2 is similar to Figure 1, so its height and radius are proportional to those of Figure 1. Let the height of Figure 2 be h inches and the radius be r inches. Then we have:
h/r = 9/4.5 = 2
So the height of Figure 2 is twice the radius.
The circumference of the base of Figure 2 is 2πr, which is equal to 2π(4.5) = 9π inches.
The area of the base of Figure 2 is πr², which is equal to π(4.5²) = 20.25π square inches.
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Answer:
The circumference of the base of figure 2 is 5 π inches, and the area of the base of figure 2 is 6.25 π square inches.
Hope this helps!
Step-by-step explanation:
The cylinders are similar, not congruent. That means the shape is the same but the values are not. The radius of figure 1 ( 4.5 in ) is half of figure 1's height ( 9 in ). That means we can figure out that figure 2's radius will also be half its height ( 5 in ), figure 2's radius is 2.5 in. Plug 2.5 into the circumference and area formulas and you have figure 2's circumference and circle area.
Work out the highest common factor (HCF) of 8 and 20.
Answer: The HCF of 8 and 20 is 4. The factors of 8 are 1, 2, 4, 8, and the factors of 20 are 1, 2, 4, 5, 10, 20.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
solve the equation 25a=10a squared
Answer: The answer is [tex]\frac{5}{2}[/tex].
Step-by-step explanation:
We are given
25a = 10[tex]a^{2}[/tex].
First, we divide both sides by a
25 = 10a
Then we divide both sides by 10
[tex]\frac{5}{2}[/tex] = a
help me please i need help im fsilinh
Answer:
b. 1/4
Step-by-step explanation:
Probability of rolling even number = 3/6 = 1/2
Probability of tails = 1/2
Multiplying these two probabilities, we have 1/4.
Helpppp
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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Find the quotient. 98.3÷7 7598.3
Hunter's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Based on the line of best fit, what quiz score should someone who studied 6 hours expect?
Therefore, we can say that after studying 2.5 hours, a student should expect a quiz score of 81.6 based on the line of best fit.
What is line of best fit?A line of best fit, also known as a trend line, is a straight line that is drawn through a scatter plot to represent the general trend or pattern of the data. It is used to show the relationship between two variables, usually the independent variable (x) and the dependent variable (y), by fitting a line that comes as close as possible to all the data points. The line of best fit can be used to make predictions about future data points or to estimate values of the dependent variable for certain values of the independent variable. The most common method for finding the line of best fit is the method of least squares, which minimizes the sum of the squared differences between the actual data points and the predicted values of the dependent variable on the line.
Here,
The point (2.5, 81.6) represents a data point on the coordinate axes, where the x-coordinate of 2.5 represents the number of hours studied and the y-coordinate of 81.6 represents the quiz score earned by a student who studied for 2.5 hours.
Based on the line of best fit that the math teacher drew, we can use this point to estimate the quiz score for other students who also study for 2.5 hours. The line of best fit is a straight line that passes through the average point of all the data points and is used to predict one variable (quiz score) based on another variable (hours studied).
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Complete question:
Hunter's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. What does the point (2.5,81.6) represent?
After studying 81.6 hours, a student should expect a score of 2.5. A student who actually spent 81.6 hours studying and got a score of
2.5. A student who actually spent 2.5 hours studying and got a score of 81.6. After studying 2.5 hours, a student should expect a score of 81.6.
A company starts to track the number of phone calls recived each month. Infromation about the number of phone calls the company recived the first three months of tracking is listed below.
-During the first month, the company recieved 4,264 phone calls.
-during the second months, the company recieved 25% more phone calls than in the first month.
-during the third month, the company recived 6,396 phone calls
What was the percent in crease in the number of phone calls from the second month to the third month?
The number of phone calls received in the second month is 25% more than the first month, which means:
Number of phone calls in second month = 1.25 x 4,264 = 5,330
To find the percent increase from the second month to the third month, we can use the percent increase formula:
Percent increase = (New value - Old value) / Old value x 100%
Using this formula, the percent increase from the second month to the third month is:
Percent increase = (6,396 - 5,330) / 5,330 x 100%
= 20%
Therefore, the percent increase in the number of phone calls from the second month to the third month is 20%.
A packaging employee making $20
per hour can package 160 items
during that hour. The direct
material cost is $.50 per item. What
is the total direct cost of 1 item?
Answer:
To find the total direct cost of one item, we need to calculate the sum of the direct labor cost and the direct material cost.
Direct labor cost per item = (hourly rate)/(number of items per hour) = $20/160 = $0.125 per item
Direct material cost per item = $0.50 per item
Total direct cost per item = direct labor cost per item + direct material cost per item
= $0.125 + $0.50 = $0.625
Therefore, the total direct cost of one item is $0.625.
The mean per capita income is 21,699
dollars per annum with a standard deviation of 835
dollars per annum.
What is the probability that the sample mean would be less than 21583
dollars if a sample of 399
persons is randomly selected? Round your answer to four decimal places.
The probability that the sample mean would be less than 21583 dollars if a sample of 399 persons is randomly selected is approximately 0.0826 or 8.26% (rounded to four decimal places).
What is probability?
Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty that the occurrence will occur.
We can use the central limit theorem (CLT) to approximate the sampling distribution of the sample mean. According to CLT, if we have a large enough sample size (n≥30), the sampling distribution of the sample mean will be approximately normal, regardless of the underlying distribution of the population.
The mean of the sampling distribution of the sample mean is the same as the population mean, which is given as μ = 21699 dollars per annum. The standard deviation of the sampling distribution of the sample mean is equal to the standard error of the mean (SEM), which is calculated as follows:
SEM = σ/√n, where n is the sample size, and is the total standard deviation.
With the numbers from the problem substituted, we obtain:
SEM = 835/√399 = 41.767
Now, we need to find the probability that the sample mean would be less than 21583 dollars. We can standardize the sample mean using the standard normal distribution as follows:
z = (x - μ) / SEM, where the sample mean is x.
Substituting the values, we get:
z = (21583 - 21699) / 41.767 = -1.389
Using a standard normal distribution table, we can find that the area to the left of z=-1.389 is 0.0826.
Therefore, the probability that the sample mean would be less than 21583 dollars if a sample of 399 persons is randomly selected is approximately 0.0826 or 8.26% (rounded to four decimal places).
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If an item has an original price of $90 and has been discounted 30%, what is the sale price
Answer: 63 US$
Step-by-step explanation:
a bakery has 3 types of pie.. apple, cherry, and peach. there are 4 times as many apple pie as peach pie. what is a possible percentages for each type of pie
Answer:
Apple Pie = 66.67%
Cherry Pie = 16.67%
Peach Pie = 16.67%
A possible distribution of pie percentages could be 66.67% apple, 16.67% cherry, and 16.67% peach.
Step-by-step explanation:
Let's assume that the bakery has 1 peach pie. Then, according to the problem statement, the bakery has 4 apple pies.
So, the total number of pies is 1 + 4 + 1 = 6.
To find the percentage of each type of pie, we need to divide the number of each type of pie by the total number of pies and multiply by 100%.
Percentage of apple pies: (4/6) x 100% = 66.67%
Percentage of cherry pies: (1/6) x 100% = 16.67%
Percentage of peach pies: (1/6) x 100% = 16.67%
Therefore, a possible distribution of pie percentages could be 66.67% apple, 16.67% cherry, and 16.67% peach.
It is important to note that this is just one possible distribution based on the information given in the problem. If we were given different information, such as the total number of pies, the percentages could be different.
1/3 ÷ 4 show your work
Answer:
Forma exacta:
1
12
Forma decimal:
0.083
Step-by-step explanation:
Answer:
[tex] \frac{1}{12} [/tex]
[tex]0.8333... [/tex]
as decimal form
Can you solve this question?
A) f'(x)=?
B) slope at x=2: ?
slope at x=3: ?
C) tangent line at x=2: y= ?
tangent line at x=3: y= ?
D) value(s) of x=?
A. The derivative of f'(x) = 26x + 5is 26x + 5
B. Slope at x = 2 is 57
Slope at x = 3 is 83
c. The equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.
D. The value of x where the tangent line is horizontal is x = -5/26.
How to calculate the value(A) f'(x) = 26x + 5.
It should be noted that to find the derivative of f(x), we apply the power rule and the constant multiple rule:
f'(x) = d/dx (13x²+5x)
= d/dx (13x²) + d/dx (5x)
= 26x + 5
(B) ain this case, to find the slope of the graph of f(x) at x = 2 and x = 3, we plug these values into the derivative:
Slope at x = 2: f'(2) = 26(2) + 5 = 57
Slope at x = 3: f'(3) = 26(3) + 5 = 83
(C) Based on the information, to find the equation for the tangent line at x = 2 and x = 3, we use the point-slope form of a line:
Tangent line at x = 2:
We know the slope is 57, and the point (2, f(2)) is on the line.
Plugging in x = 2 to f(x) gives us f(2) = 13(2)² + 5(2) = 58.
So the equation of the tangent line at x = 2 is y - 58 = 57(x - 2), or y = 57x - 56.
Tangent line at x = 3:
We know the slope is 83, and the point (3, f(3)) is on the line.
Plugging in x = 3 to f(x) gives us f(3) = 13(3)² + 5(3) = 122.
So the equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.
D. In order to find where the tangent line is horizontal, we need to find where the slope is equal to zero. Setting f'(x) = 0 and solving for x gives:
f'(x) = 26x + 5 = 0
x = -5/26
Therefore, the only value of x where the tangent line is horizontal is x = -5/26.
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13. Higher Order Thinking Name two rays with the same endpoint in the figure below. Do they form an angle? Explain.
The two rays with the same endpoint in the figure below are AB and BC. Although they share a common endpoint (B), they do not form an angle since they are collinear and lie on the same line. Two non-collinear rays that share an endpoint create an angle. In this case, AB and BC lie on line AC and do not form an angle.
An angle is formed by two rays that originate from a common endpoint. In the given figure, AB and BC share the same endpoint (B), but they do not form an angle since they lie on the same line. A line is an infinite set of points that extends in both directions, while a ray is a portion of a line that starts at a particular point and extends infinitely in one direction. When two rays share a common endpoint, they form an angle only if they are not collinear, i.e., they do not lie on the same line. In this case, since AB and BC lie on line AC, they do not form an angle. Therefore, AB and BC are collinear and do not form an angle.
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Solve For B. 47.5 degrees, 79.5 degrees
53 is the answer
47.5 + 79.5= 127
180-127=53
The distances, in light years, of four stars from a space probe are shown. Put the stars in order from the closest one (least distance) to the farthest one (greatest distance). 0.886 0.883 1.25 0.89
A.
0.883, 0.886, 0.89, 1.25
B.
0.883, 0.886, 1.25, 0.89
C.
1.25, 0.89, 0.886, 0.883
D.
0.886, 0.883, 0.89, 1.25
The stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.
That means we need to start with the smallest value and move toward the largest value.
Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.
Putting the given distances in ascending order, we get:
0.883, 0.886, 0.89, 1.25
Therefore, the stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
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area of a triangle vertices are (-3,1), (1,1) and (1,4)
The area of the triangle is 3 square units whose vertices are (-3,1), (1,1) and (1,4). We will use distance formulae in this question.
To find the area of a triangle whose vertices are (-3,1), (1,1), and (1,4), we can use the formula for the area of a triangle:
Area = 1/2 * base * height
where the base and height are perpendicular and are formed by any two sides of the triangle.
To apply this formula, we can choose the line segment between (1,1) and (1,4) as the base of the triangle, since it is a vertical line and therefore has a length equal to the height of the triangle. The length of this line segment is 4 - 1 = 3 units.
Next, we need to find the length of the perpendicular segment from the point (-3,1) to the line containing the base. To do this, we can use the formula for the distance between a point and a line:
distance = [tex]|ax + by + c| / \sqrt{(a^2 + b^2)[/tex]
where a, b, and c are the coefficients of the equation of the line and x, y are the coordinates of the point.
In this case, the equation of the line containing the base is x = 1, so a = 1, b = 0, and c = -1. Plugging in the coordinates of (-3,1), we get:
distance = [tex]|1*(-3) + 0*(1) - 1| / \sqrt{(1^2 + 0^2)} = 2[/tex]
Therefore, the height of the triangle is 2 units.
Finally, we can plug these values into the formula for the area of a triangle to get:
Area = 1/2 * base * height = 1/2 * 3 * 2 = 3
So the area of the triangle is 3 square units.
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Sin ² 20 +Sin² 40° +Sin ²80 simplify
Answer:
The answer is 1.5
Step-by-step explanation:
You just calculate in calculator and you will get the answer as 1.5
Seven different single-digit numbers are written in the circles of the diagram shown with one number in each circle. The product of the three numbers in each of the three lines of three numbers is the same. Which number is written in the circle containing the question mark?
Answer:
Without an image or a more detailed description of the diagram, it's difficult to provide an exact answer to this problem. However, we can use some logical reasoning to try to solve it.
Let's assume that the three lines of three numbers are arranged in a Tic-Tac-Toe grid, like this:
CSS
Copy code
A B C
D E F
G H I
We know that the product of the three numbers in each line is the same. Let's call this product "P". Then we can write:
CSS
Copy code
A * B * C = P
D * E * F = P
G * H * I = P
If we divide the second equation by the first equation, we get:
CSS
Copy code
(D * E * F) / (A * B * C) = 1
Since all the numbers are single-digit, this means that either D or F is equal to A, B, C, or 1. If D or F is equal to 1, then E is also equal to 1, which means that the entire middle row is filled with 1s, and that cannot be the case since all the numbers are different.
Therefore, we can assume that either D or F is equal to one of the numbers in the top row. Without further information, we cannot determine which one it is, but we know that the product of the numbers in the bottom row must be divisible by the product of the numbers in the top row. This means that the number in the circle containing the question mark must be a factor of this product, and it must be different from all the other numbers in the diagram.
Again, without more information, we cannot determine the exact number in the circle containing the question mark, but this logic should help narrow down the possibilities.
Step-by-step explanation:
slove the trig problems using the ratios. Remember to use SOH-CAH-TOA
1. solve for side x x = ___
2.solve for side x x = ___
3. solve for angle x x = ____
4. solve for angle x x = ____
thank you
Answer:
Step-by-step explanation:
.The regression coefficient of Y on X = 1.2 . If
=
−100
2
=
−100
3
, find .
For the regression coefficient, the value of bvu is 0.8.
How to find bvu?Regression coefficient is a measure of the relationship between two variables in a regression analysis. It represents the degree of change in one variable for a unit change in another variable.
Recall that:
u = (x – a)/p
v = (y – c)/q
b[tex]_{yx}[/tex] = q/p × bvu
Given: u = (x-100)/2 and v = (y-200)/3
Thus, q = 3 and p = 2
Since the regression coefficient of Y on X = 1.2.
Thus, b[tex]_{yx}[/tex] = 1.2
b[tex]_{yx}[/tex] = q/p × bvu
1.2 = 3/2 * bvu
bvu = 1.2 * 2/3
Therefore, the value of bvu is 0.8
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Complete Question
The coefficient of regression on Y on X = 1.2.
If U = (x-100)/2 and V = (y-200)/3 .
Find bvu.